Rockfish Historical Harvest Estimates

This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.

Issue	Howard	Bayes
Time series	1999 - present	1977 - present
Bias in SWHS	Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests.	Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases	Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data.	Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations	Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas.	Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation	Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with.	By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

   1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
   2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
   3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

• Model: LB_fit_3pH

• Model Run: rf_harvest_est_nm_wt_thru2023_1500000_nm_wts_sd7_2025-06-02 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9967

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Model fit

Logbook residuals

Figure 18.- Residuals from logbook harvests.

SWHS residuals

Figure 19.- Residuals from SWHS harvests.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 21.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

## NULL

## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(slope|non-pelagic & non-yellowye) For release estimates

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Weight Fits

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

### Summary of unconverged parameters:

##  [1] "re_pelagic"     "Ro_ayu"         "Ro_ay"          "Ry_ayu"        
##  [5] "Ry_ayu_mort"    "Ry_ay"          "Ry_ay_mort"     "Rs_ayu"        
##  [9] "Rs_ayu_mort"    "By_ayu"         "beta2_pH"       "Ro_ayg"        
## [13] "By_ayg"         "Ho_ayu"         "Ty_ayu"         "Ho_ayg"        
## [17] "p_pelagic"      "Ry_ayg"         "Ry_ayg_mort"    "re_yellow"     
## [21] "beta1_pH"       "Hb_ayu"         "H_ayu"          "Rb_ayu"        
## [25] "Rb_ayu_mort"    "Hp_ayu"         "Rp_ayu"         "Rp_ayu_mort"   
## [29] "R_ayu"          "Rb_ay_mort"     "Rb_ay"          "By_ay"         
## [33] "Rp_ay_mort"     "Rp_ay"          "R_ay"           "Hb_ay"         
## [37] "p_dsr"          "Hp_ay"          "H_ay"           "Hdnye_ay"      
## [41] "Bb_ayg"         "tau_beta4_pH"   "pH"             "Tdnye_ay"      
## [45] "Ho_ay"          "Rd_ayu"         "Bdnye_ay"       "Tb_ayu"        
## [49] "Ty_ay"          "Rdnye_ayu"      "Rdnye_ayu_mort" "Rd_ay"         
## [53] "Hy_ayg"         "Tp_ayu"

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta3_yellow 1 1.530327 beta2_pelagic 2 1.320649 beta0_pelagic 2 1.320364 beta2_pH 1 1.228612 beta1_pelagic 2 1.205686

parameter n badRhat_avg beta3_pelagic 1 1.195056 beta1_pH 2 1.144039 beta0_yellow 1 1.130892 beta4_pelagic 1 1.121008

Table 2. Summary of unconverged major parameters by area

Parameter	CI	NG	PWSI	PWSO	BSAI	SOKO2SAP	WKMA	afognak	eastside	northeast	CSEO	EWYKT	NSEI	NSEO	SSEI	SSEO
beta1_pH	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0
beta1_pH	0	0	0	0	1	1	0	0	0	0	0	0	0	0	0	0
beta2_pH	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
beta2_pH	0	0	0	0	0	0	1	0	0	0	0	0	0	0	0	0
H_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
H_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Hb_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Hb_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Hdnye_ay	0	0	0	0	0	0	0	0	0	0	9	0	0	0	0	0
Ho_ay	0	0	0	0	0	0	0	0	0	0	4	0	0	0	0	0
Ho_ayg	0	0	0	0	3	0	0	0	0	0	0	0	0	0	0	0
Ho_ayu	0	0	0	0	0	0	0	0	3	0	0	0	0	0	0	0
Hp_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Hp_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Hy_ayg	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
p_dsr	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0	0
p_pelagic	0	0	0	0	0	0	0	0	0	0	25	0	0	0	0	0
pH	0	0	0	0	0	0	0	0	0	0	0	0	3	0	0	0
R_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
R_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rb_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rb_ay_mort	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rb_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rb_ayu_mort	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rd_ay	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
Rd_ayu	0	0	0	0	0	0	0	0	0	0	0	2	0	0	0	0
Rdnye_ayu	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
Rdnye_ayu_mort	0	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0
re_pelagic	0	0	0	0	0	0	0	0	0	0	36	0	0	0	0	0
Ro_ay	0	0	0	0	13	10	1	2	0	0	0	0	0	0	0	0
Ro_ayg	0	0	0	0	3	1	0	1	1	0	0	0	0	0	0	0
Ro_ayu	0	0	0	1	14	12	1	2	0	1	0	1	0	0	0	0
Rp_ay	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rp_ay_mort	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rp_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rp_ayu_mort	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
Rs_ayu	0	0	0	0	0	0	0	0	0	0	1	3	0	0	0	0
Rs_ayu_mort	0	0	0	0	0	0	0	0	0	0	1	3	0	0	0	0
Ry_ay	0	0	0	0	7	3	4	1	2	0	0	1	0	0	0	0
Ry_ay_mort	0	0	0	0	7	3	4	1	2	0	0	1	0	0	0	0
Ry_ayg	0	0	0	0	1	1	0	0	1	0	0	1	0	0	0	0
Ry_ayg_mort	0	0	0	0	1	1	0	0	1	0	0	1	0	0	0	0
Ry_ayu	0	0	0	1	8	3	7	1	2	0	0	2	0	0	0	0
Ry_ayu_mort	0	0	0	1	8	3	7	1	2	0	0	2	0	0	0	0
tau_beta4_pH	1	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0
Tp_ayu	0	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0
beta0_pelagic	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0
beta0_yellow	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
beta1_pelagic	0	0	0	1	0	0	0	0	0	0	1	0	0	0	0	0
beta2_pelagic	0	0	0	0	0	0	0	0	0	0	1	0	1	0	0	0
beta3_pelagic	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
beta3_yellow	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
beta4_pelagic	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.124	0.073	-0.255	-0.126	0.027
mu_bc_H[2]	-0.097	0.045	-0.175	-0.100	0.001
mu_bc_H[3]	-0.433	0.070	-0.567	-0.433	-0.292
mu_bc_H[4]	-0.986	0.193	-1.366	-0.981	-0.610
mu_bc_H[5]	0.895	0.873	-0.188	0.718	3.082
mu_bc_H[6]	-2.145	0.319	-2.747	-2.150	-1.495
mu_bc_H[7]	-0.457	0.106	-0.677	-0.453	-0.254
mu_bc_H[8]	0.236	0.363	-0.364	0.196	1.069
mu_bc_H[9]	-0.291	0.133	-0.548	-0.295	-0.018
mu_bc_H[10]	-0.101	0.071	-0.236	-0.103	0.043
mu_bc_H[11]	-0.122	0.038	-0.193	-0.122	-0.046
mu_bc_H[12]	-0.250	0.105	-0.466	-0.247	-0.048
mu_bc_H[13]	-0.136	0.078	-0.283	-0.140	0.017
mu_bc_H[14]	-0.303	0.094	-0.495	-0.300	-0.127
mu_bc_H[15]	-0.342	0.050	-0.438	-0.343	-0.242
mu_bc_H[16]	-0.254	0.384	-0.900	-0.290	0.624
mu_bc_R[1]	1.319	0.141	1.031	1.318	1.596
mu_bc_R[2]	1.454	0.095	1.262	1.455	1.638
mu_bc_R[3]	1.391	0.146	1.101	1.394	1.667
mu_bc_R[4]	0.913	0.200	0.491	0.925	1.274
mu_bc_R[5]	1.213	0.461	0.256	1.226	2.100
mu_bc_R[6]	-1.605	0.413	-2.461	-1.598	-0.815
mu_bc_R[7]	0.436	0.210	-0.009	0.445	0.822
mu_bc_R[8]	0.531	0.186	0.161	0.535	0.890
mu_bc_R[9]	0.329	0.203	-0.117	0.340	0.707
mu_bc_R[10]	1.311	0.171	0.951	1.319	1.625
mu_bc_R[11]	1.038	0.097	0.849	1.036	1.228
mu_bc_R[12]	0.820	0.200	0.423	0.823	1.211
mu_bc_R[13]	1.027	0.105	0.819	1.030	1.230
mu_bc_R[14]	0.897	0.145	0.610	0.898	1.174
mu_bc_R[15]	0.780	0.110	0.554	0.783	0.997
mu_bc_R[16]	1.095	0.128	0.838	1.092	1.349
tau_pH[1]	5.119	0.440	4.296	5.112	6.000
tau_pH[2]	1.974	0.228	1.561	1.966	2.449
tau_pH[3]	2.145	0.218	1.754	2.136	2.603
beta0_pH[1,1]	0.574	0.172	0.223	0.578	0.903
beta0_pH[2,1]	1.371	0.174	1.019	1.373	1.702
beta0_pH[3,1]	1.415	0.202	0.957	1.427	1.774
beta0_pH[4,1]	1.555	0.218	1.078	1.566	1.946
beta0_pH[5,1]	-0.861	0.287	-1.489	-0.841	-0.341
beta0_pH[6,1]	-0.730	0.498	-2.056	-0.641	-0.074
beta0_pH[7,1]	-0.394	0.500	-1.587	-0.361	0.558
beta0_pH[8,1]	-0.681	0.301	-1.377	-0.640	-0.207
beta0_pH[9,1]	-0.620	0.273	-1.206	-0.600	-0.142
beta0_pH[10,1]	0.353	0.203	-0.054	0.358	0.736
beta0_pH[11,1]	-0.093	0.171	-0.431	-0.094	0.233
beta0_pH[12,1]	0.481	0.187	0.107	0.483	0.843
beta0_pH[13,1]	0.003	0.147	-0.284	0.005	0.292
beta0_pH[14,1]	-0.312	0.170	-0.652	-0.309	0.019
beta0_pH[15,1]	-0.048	0.181	-0.403	-0.045	0.298
beta0_pH[16,1]	-0.495	0.392	-1.523	-0.423	0.060
beta0_pH[1,2]	2.837	0.158	2.520	2.843	3.140
beta0_pH[2,2]	2.889	0.138	2.605	2.891	3.153
beta0_pH[3,2]	3.133	0.151	2.851	3.130	3.451
beta0_pH[4,2]	2.955	0.138	2.676	2.955	3.227
beta0_pH[5,2]	4.792	1.427	3.003	4.481	8.553
beta0_pH[6,2]	3.119	0.208	2.723	3.117	3.534
beta0_pH[7,2]	1.833	0.198	1.449	1.836	2.222
beta0_pH[8,2]	2.869	0.174	2.522	2.869	3.205
beta0_pH[9,2]	3.438	0.222	3.004	3.441	3.867
beta0_pH[10,2]	3.692	0.214	3.269	3.697	4.106
beta0_pH[11,2]	-4.835	0.299	-5.394	-4.831	-4.231
beta0_pH[12,2]	-4.785	0.384	-5.542	-4.781	-4.044
beta0_pH[13,2]	-4.588	0.403	-5.367	-4.599	-3.781
beta0_pH[14,2]	-5.567	0.477	-6.568	-5.555	-4.704
beta0_pH[15,2]	-4.313	0.347	-4.983	-4.319	-3.618
beta0_pH[16,2]	-4.870	0.395	-5.662	-4.860	-4.121
beta0_pH[1,3]	-0.150	0.718	-1.809	-0.065	1.018
beta0_pH[2,3]	2.186	0.161	1.869	2.185	2.505
beta0_pH[3,3]	2.528	0.149	2.229	2.526	2.810
beta0_pH[4,3]	2.962	0.159	2.654	2.961	3.275
beta0_pH[5,3]	2.188	1.366	0.409	1.895	5.680
beta0_pH[6,3]	0.992	0.508	-0.225	1.023	1.896
beta0_pH[7,3]	0.635	0.173	0.297	0.634	0.983
beta0_pH[8,3]	0.307	0.193	-0.067	0.305	0.680
beta0_pH[9,3]	-0.642	0.385	-1.607	-0.609	0.008
beta0_pH[10,3]	0.462	0.391	-0.535	0.509	1.095
beta0_pH[11,3]	-0.178	0.331	-0.832	-0.186	0.511
beta0_pH[12,3]	-0.834	0.352	-1.586	-0.809	-0.222
beta0_pH[13,3]	-0.158	0.321	-0.773	-0.159	0.452
beta0_pH[14,3]	-0.275	0.266	-0.787	-0.280	0.254
beta0_pH[15,3]	-0.651	0.262	-1.161	-0.648	-0.161
beta0_pH[16,3]	-0.393	0.286	-0.941	-0.390	0.164
beta1_pH[1,1]	3.048	0.311	2.475	3.029	3.708
beta1_pH[2,1]	2.172	0.283	1.689	2.155	2.812
beta1_pH[3,1]	1.993	0.330	1.434	1.962	2.724
beta1_pH[4,1]	2.408	0.350	1.837	2.367	3.224
beta1_pH[5,1]	2.292	0.346	1.703	2.263	3.054
beta1_pH[6,1]	3.828	1.161	2.301	3.569	6.748
beta1_pH[7,1]	2.409	0.969	0.629	2.335	4.689
beta1_pH[8,1]	4.012	0.999	2.617	3.808	6.412
beta1_pH[9,1]	2.292	0.356	1.688	2.257	3.076
beta1_pH[10,1]	2.224	0.281	1.714	2.213	2.812
beta1_pH[11,1]	3.275	0.214	2.867	3.270	3.705
beta1_pH[12,1]	2.557	0.216	2.133	2.554	2.975
beta1_pH[13,1]	2.974	0.214	2.556	2.972	3.405
beta1_pH[14,1]	3.415	0.222	2.993	3.407	3.870
beta1_pH[15,1]	2.553	0.230	2.100	2.546	3.016
beta1_pH[16,1]	4.114	0.689	3.189	3.969	5.881
beta1_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,2]	0.000	0.001	0.000	0.000	0.001
beta1_pH[4,2]	0.000	0.001	0.000	0.000	0.001
beta1_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta1_pH[11,2]	6.682	0.337	5.987	6.686	7.313
beta1_pH[12,2]	6.445	0.451	5.578	6.435	7.401
beta1_pH[13,2]	6.964	0.441	6.097	6.967	7.802
beta1_pH[14,2]	7.206	0.497	6.297	7.185	8.216
beta1_pH[15,2]	6.781	0.382	6.042	6.788	7.523
beta1_pH[16,2]	7.452	0.437	6.651	7.436	8.349
beta1_pH[1,3]	4.685	1.630	2.149	4.447	8.102
beta1_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[5,3]	3.243	3.189	0.750	2.786	8.637
beta1_pH[6,3]	3.022	2.558	0.453	2.651	8.608
beta1_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta1_pH[8,3]	2.751	0.344	2.065	2.743	3.418
beta1_pH[9,3]	2.768	0.455	1.983	2.730	3.859
beta1_pH[10,3]	2.906	0.470	2.142	2.844	4.063
beta1_pH[11,3]	2.764	0.384	2.003	2.762	3.539
beta1_pH[12,3]	4.086	0.439	3.281	4.064	4.993
beta1_pH[13,3]	1.748	0.344	1.077	1.744	2.426
beta1_pH[14,3]	2.537	0.341	1.865	2.542	3.204
beta1_pH[15,3]	1.953	0.295	1.401	1.953	2.549
beta1_pH[16,3]	1.806	0.322	1.181	1.810	2.445
beta2_pH[1,1]	0.489	0.129	0.297	0.469	0.791
beta2_pH[2,1]	0.575	0.373	0.233	0.513	1.219
beta2_pH[3,1]	0.623	0.419	0.210	0.539	1.569
beta2_pH[4,1]	0.475	0.199	0.207	0.439	0.943
beta2_pH[5,1]	1.410	0.934	0.239	1.272	3.689
beta2_pH[6,1]	0.184	0.068	0.082	0.174	0.341
beta2_pH[7,1]	0.087	1.155	0.000	0.000	0.324
beta2_pH[8,1]	0.241	0.086	0.122	0.226	0.452
beta2_pH[9,1]	0.438	0.202	0.177	0.399	0.931
beta2_pH[10,1]	0.585	0.222	0.277	0.547	1.113
beta2_pH[11,1]	0.790	0.207	0.486	0.760	1.286
beta2_pH[12,1]	1.334	0.462	0.719	1.242	2.448
beta2_pH[13,1]	0.743	0.224	0.414	0.712	1.294
beta2_pH[14,1]	0.835	0.207	0.536	0.799	1.335
beta2_pH[15,1]	0.798	0.308	0.402	0.736	1.546
beta2_pH[16,1]	0.385	0.178	0.170	0.342	0.838
beta2_pH[1,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[2,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,2]	-2.081	1.903	-7.057	-1.602	-0.024
beta2_pH[4,2]	-2.073	1.898	-6.994	-1.576	-0.029
beta2_pH[5,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[6,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[7,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[9,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[10,2]	0.000	0.000	0.000	0.000	0.000
beta2_pH[11,2]	-9.622	4.532	-21.216	-8.626	-4.039
beta2_pH[12,2]	-8.220	5.254	-21.133	-7.243	-1.054
beta2_pH[13,2]	-7.984	5.227	-20.869	-6.865	-1.680
beta2_pH[14,2]	-8.777	4.977	-21.336	-7.614	-2.533
beta2_pH[15,2]	-9.470	4.591	-21.026	-8.417	-3.864
beta2_pH[16,2]	-9.711	4.621	-21.174	-8.719	-3.964
beta2_pH[1,3]	0.247	0.320	0.101	0.178	0.732
beta2_pH[2,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[3,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[4,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[5,3]	8.822	6.145	-0.147	7.991	22.787
beta2_pH[6,3]	8.792	6.036	0.155	7.819	22.730
beta2_pH[7,3]	0.000	0.000	0.000	0.000	0.000
beta2_pH[8,3]	9.717	5.436	1.968	8.699	22.669
beta2_pH[9,3]	8.583	5.976	0.487	7.641	22.278
beta2_pH[10,3]	8.161	6.142	0.494	7.265	22.143
beta2_pH[11,3]	-2.255	2.074	-8.040	-1.675	-0.614
beta2_pH[12,3]	-2.400	2.001	-7.689	-1.863	-0.946
beta2_pH[13,3]	-2.799	2.346	-9.163	-2.091	-0.704
beta2_pH[14,3]	-2.791	2.270	-9.099	-2.094	-0.843
beta2_pH[15,3]	-2.950	2.259	-9.342	-2.224	-1.032
beta2_pH[16,3]	-2.979	2.405	-9.965	-2.193	-0.922
beta3_pH[1,1]	35.962	0.834	34.404	35.941	37.729
beta3_pH[2,1]	33.692	1.273	31.574	33.572	36.536
beta3_pH[3,1]	33.625	1.131	31.497	33.570	36.027
beta3_pH[4,1]	33.800	1.215	31.555	33.702	36.369
beta3_pH[5,1]	27.689	1.087	26.408	27.458	30.992
beta3_pH[6,1]	38.229	3.302	32.312	38.029	45.035
beta3_pH[7,1]	31.197	8.106	18.552	30.797	45.220
beta3_pH[8,1]	39.851	2.143	36.115	39.656	44.783
beta3_pH[9,1]	30.752	1.471	28.117	30.668	33.869
beta3_pH[10,1]	33.009	1.004	31.164	32.952	35.105
beta3_pH[11,1]	30.320	0.462	29.424	30.325	31.242
beta3_pH[12,1]	30.161	0.403	29.352	30.171	30.947
beta3_pH[13,1]	33.190	0.592	32.066	33.175	34.371
beta3_pH[14,1]	32.036	0.461	31.163	32.027	32.982
beta3_pH[15,1]	31.128	0.652	29.834	31.126	32.370
beta3_pH[16,1]	31.952	1.038	30.232	31.817	34.394
beta3_pH[1,2]	29.885	7.908	18.578	28.743	44.923
beta3_pH[2,2]	29.931	7.944	18.459	28.927	44.935
beta3_pH[3,2]	29.998	7.905	18.482	28.902	44.876
beta3_pH[4,2]	29.877	7.919	18.541	28.744	44.788
beta3_pH[5,2]	30.034	7.975	18.349	28.964	44.886
beta3_pH[6,2]	29.774	7.935	18.462	28.826	44.739
beta3_pH[7,2]	29.950	8.125	18.380	28.865	45.087
beta3_pH[8,2]	29.950	7.975	18.465	28.971	45.154
beta3_pH[9,2]	30.020	8.051	18.407	28.909	45.008
beta3_pH[10,2]	29.903	7.866	18.379	28.882	44.799
beta3_pH[11,2]	43.401	0.178	43.118	43.380	43.768
beta3_pH[12,2]	43.192	0.197	42.943	43.145	43.706
beta3_pH[13,2]	43.869	0.146	43.476	43.909	44.045
beta3_pH[14,2]	43.294	0.207	43.043	43.235	43.806
beta3_pH[15,2]	43.414	0.194	43.104	43.395	43.813
beta3_pH[16,2]	43.504	0.190	43.161	43.506	43.856
beta3_pH[1,3]	39.061	3.323	32.361	38.955	45.396
beta3_pH[2,3]	30.334	7.998	18.559	29.614	44.889
beta3_pH[3,3]	29.883	8.053	18.388	28.929	44.987
beta3_pH[4,3]	30.370	8.002	18.410	29.719	44.855
beta3_pH[5,3]	36.784	3.888	31.278	36.237	45.065
beta3_pH[6,3]	40.302	3.548	31.646	40.688	45.605
beta3_pH[7,3]	38.007	4.354	31.312	37.811	45.634
beta3_pH[8,3]	41.497	0.257	41.062	41.490	41.950
beta3_pH[9,3]	33.467	0.580	31.648	33.554	34.258
beta3_pH[10,3]	35.763	0.870	33.246	36.002	36.840
beta3_pH[11,3]	41.799	0.794	40.190	41.818	43.243
beta3_pH[12,3]	41.713	0.387	40.962	41.729	42.447
beta3_pH[13,3]	42.797	0.913	41.062	42.799	45.016
beta3_pH[14,3]	41.098	0.585	39.857	41.123	42.170
beta3_pH[15,3]	42.521	0.636	41.138	42.583	43.599
beta3_pH[16,3]	42.887	0.730	41.258	42.988	44.066
beta0_pelagic[1]	2.228	0.130	1.968	2.228	2.476
beta0_pelagic[2]	1.517	0.126	1.266	1.520	1.770
beta0_pelagic[3]	-0.813	0.770	-2.485	-0.757	0.408
beta0_pelagic[4]	-0.694	0.834	-2.516	-0.621	0.629
beta0_pelagic[5]	1.189	0.251	0.699	1.189	1.670
beta0_pelagic[6]	1.473	0.271	0.887	1.498	1.948
beta0_pelagic[7]	1.602	0.215	1.190	1.596	2.051
beta0_pelagic[8]	1.761	0.202	1.368	1.758	2.165
beta0_pelagic[9]	2.469	0.310	1.867	2.468	3.038
beta0_pelagic[10]	2.507	0.210	2.052	2.514	2.893
beta0_pelagic[11]	0.093	0.398	-0.722	0.116	0.746
beta0_pelagic[12]	1.681	0.145	1.390	1.685	1.957
beta0_pelagic[13]	0.319	0.182	-0.083	0.330	0.650
beta0_pelagic[14]	-0.122	0.313	-0.876	-0.079	0.346
beta0_pelagic[15]	-0.265	0.136	-0.511	-0.268	0.009
beta0_pelagic[16]	0.214	0.315	-0.533	0.293	0.653
beta1_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta1_pelagic[3]	2.616	1.262	0.669	2.473	5.528
beta1_pelagic[4]	2.228	1.106	0.605	2.089	4.784
beta1_pelagic[5]	-0.079	0.313	-0.701	-0.078	0.539
beta1_pelagic[6]	-0.102	0.456	-0.873	-0.151	0.748
beta1_pelagic[7]	-0.031	0.293	-0.585	-0.028	0.545
beta1_pelagic[8]	-0.002	0.279	-0.549	-0.013	0.588
beta1_pelagic[9]	0.219	0.488	-0.753	0.346	0.962
beta1_pelagic[10]	0.063	0.270	-0.466	0.060	0.609
beta1_pelagic[11]	3.733	1.119	2.133	3.636	6.247
beta1_pelagic[12]	2.790	0.330	2.194	2.775	3.428
beta1_pelagic[13]	2.921	0.714	1.805	2.827	4.501
beta1_pelagic[14]	4.430	1.033	2.890	4.241	6.873
beta1_pelagic[15]	2.917	0.253	2.439	2.906	3.424
beta1_pelagic[16]	3.912	1.113	2.715	3.474	6.784
beta2_pelagic[1]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[2]	0.000	0.000	0.000	0.000	0.000
beta2_pelagic[3]	0.315	1.269	0.030	0.100	1.662
beta2_pelagic[4]	0.838	2.314	0.028	0.257	7.592
beta2_pelagic[5]	-0.014	0.654	-1.381	-0.022	1.354
beta2_pelagic[6]	-0.100	0.686	-1.500	-0.147	1.316
beta2_pelagic[7]	0.004	0.647	-1.365	0.004	1.344
beta2_pelagic[8]	0.000	0.618	-1.232	-0.013	1.325
beta2_pelagic[9]	0.183	0.671	-1.268	0.244	1.501
beta2_pelagic[10]	0.015	0.563	-1.173	0.026	1.211
beta2_pelagic[11]	1.767	3.874	0.126	0.254	12.971
beta2_pelagic[12]	5.530	4.659	0.900	4.082	18.624
beta2_pelagic[13]	0.881	1.991	0.206	0.474	4.783
beta2_pelagic[14]	0.313	0.174	0.141	0.286	0.649
beta2_pelagic[15]	5.736	4.392	1.258	4.524	17.743
beta2_pelagic[16]	3.591	5.135	0.173	1.091	18.939
beta3_pelagic[1]	29.690	7.927	18.461	28.461	44.839
beta3_pelagic[2]	29.688	7.968	18.473	28.473	44.907
beta3_pelagic[3]	28.635	6.919	18.637	27.649	43.880
beta3_pelagic[4]	24.510	5.607	18.367	23.104	42.095
beta3_pelagic[5]	30.413	8.212	18.528	29.328	45.317
beta3_pelagic[6]	31.900	6.756	19.000	31.860	44.330
beta3_pelagic[7]	29.707	7.960	18.490	28.661	44.961
beta3_pelagic[8]	29.366	7.945	18.374	27.930	44.937
beta3_pelagic[9]	31.116	5.988	19.423	31.046	43.111
beta3_pelagic[10]	29.666	8.218	18.431	28.186	44.941
beta3_pelagic[11]	42.599	2.073	37.546	43.069	45.769
beta3_pelagic[12]	43.473	0.299	42.979	43.454	44.027
beta3_pelagic[13]	42.863	1.346	40.412	42.807	45.555
beta3_pelagic[14]	42.456	1.608	39.171	42.448	45.548
beta3_pelagic[15]	43.167	0.259	42.550	43.172	43.668
beta3_pelagic[16]	43.114	0.977	40.948	43.179	45.313
mu_beta0_pelagic[1]	0.492	1.180	-2.034	0.555	2.786
mu_beta0_pelagic[2]	1.803	0.400	1.007	1.818	2.568
mu_beta0_pelagic[3]	0.315	0.473	-0.667	0.321	1.261
tau_beta0_pelagic[1]	0.348	0.369	0.048	0.229	1.371
tau_beta0_pelagic[2]	2.819	3.264	0.249	2.060	9.819
tau_beta0_pelagic[3]	1.518	1.143	0.160	1.260	4.558
beta0_yellow[1]	-0.537	0.197	-0.973	-0.517	-0.212
beta0_yellow[2]	0.498	0.169	0.150	0.504	0.798
beta0_yellow[3]	-0.333	0.234	-0.837	-0.315	0.028
beta0_yellow[4]	0.782	0.447	-0.844	0.885	1.208
beta0_yellow[5]	-0.299	0.359	-0.987	-0.288	0.402
beta0_yellow[6]	1.112	0.168	0.800	1.107	1.454
beta0_yellow[7]	0.980	0.159	0.674	0.980	1.296
beta0_yellow[8]	1.010	0.157	0.708	1.002	1.332
beta0_yellow[9]	0.661	0.159	0.342	0.663	0.977
beta0_yellow[10]	0.593	0.145	0.309	0.592	0.874
beta0_yellow[11]	-1.880	0.603	-2.901	-1.933	-0.272
beta0_yellow[12]	-3.717	0.420	-4.535	-3.696	-2.906
beta0_yellow[13]	-3.739	0.495	-4.823	-3.709	-2.872
beta0_yellow[14]	-2.080	0.631	-3.123	-2.148	-0.366
beta0_yellow[15]	-2.888	0.425	-3.713	-2.874	-2.111
beta0_yellow[16]	-2.437	0.487	-3.439	-2.441	-1.439
beta1_yellow[1]	0.817	0.987	0.012	0.657	2.922
beta1_yellow[2]	1.082	0.394	0.590	1.028	2.027
beta1_yellow[3]	0.728	0.352	0.244	0.694	1.414
beta1_yellow[4]	1.473	1.007	0.651	1.183	4.742
beta1_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta1_yellow[11]	2.117	0.580	0.735	2.129	3.183
beta1_yellow[12]	2.511	0.437	1.707	2.482	3.406
beta1_yellow[13]	2.857	0.494	2.020	2.819	3.917
beta1_yellow[14]	2.199	0.581	0.762	2.242	3.256
beta1_yellow[15]	2.137	0.414	1.363	2.126	2.944
beta1_yellow[16]	2.197	0.486	1.204	2.199	3.170
beta2_yellow[1]	-3.562	3.018	-10.844	-2.827	-0.063
beta2_yellow[2]	-3.522	2.828	-10.369	-2.825	-0.176
beta2_yellow[3]	-3.469	3.001	-11.407	-2.683	-0.123
beta2_yellow[4]	-3.075	3.125	-11.103	-2.131	-0.062
beta2_yellow[5]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[6]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[7]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[8]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[9]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[10]	0.000	0.000	0.000	0.000	0.000
beta2_yellow[11]	-4.384	2.978	-11.545	-3.830	-0.099
beta2_yellow[12]	-4.967	2.747	-11.846	-4.346	-1.253
beta2_yellow[13]	-4.807	2.618	-11.643	-4.206	-1.490
beta2_yellow[14]	-4.765	2.950	-11.833	-4.331	-0.155
beta2_yellow[15]	-4.378	2.733	-11.221	-3.713	-0.990
beta2_yellow[16]	-5.067	2.913	-12.186	-4.429	-1.300
beta3_yellow[1]	25.766	7.136	18.252	22.660	44.222
beta3_yellow[2]	29.077	1.975	24.750	28.895	32.975
beta3_yellow[3]	32.976	3.317	25.085	32.779	41.451
beta3_yellow[4]	29.093	3.721	21.506	28.054	36.214
beta3_yellow[5]	30.140	7.992	18.478	29.096	44.894
beta3_yellow[6]	30.256	7.986	18.495	29.351	45.040
beta3_yellow[7]	30.034	7.931	18.552	28.957	44.809
beta3_yellow[8]	30.066	7.838	18.462	29.182	44.861
beta3_yellow[9]	29.978	8.025	18.446	28.977	44.727
beta3_yellow[10]	29.904	7.853	18.518	28.863	44.742
beta3_yellow[11]	44.284	3.107	33.994	45.324	45.973
beta3_yellow[12]	43.307	0.386	42.521	43.288	44.053
beta3_yellow[13]	44.865	0.397	44.000	44.938	45.526
beta3_yellow[14]	43.631	2.522	33.982	44.197	45.801
beta3_yellow[15]	45.175	0.526	44.161	45.166	45.965
beta3_yellow[16]	44.575	0.654	43.386	44.576	45.834
mu_beta0_yellow[1]	0.103	0.553	-1.034	0.105	1.204
mu_beta0_yellow[2]	0.647	0.340	-0.084	0.668	1.271
mu_beta0_yellow[3]	-2.429	0.676	-3.517	-2.529	-0.807
tau_beta0_yellow[1]	1.770	2.102	0.094	1.118	7.303
tau_beta0_yellow[2]	3.621	4.542	0.305	2.438	13.117
tau_beta0_yellow[3]	1.431	2.434	0.092	0.851	6.137
beta0_black[1]	-0.078	0.161	-0.398	-0.077	0.235
beta0_black[2]	1.910	0.131	1.654	1.912	2.164
beta0_black[3]	1.320	0.137	1.054	1.317	1.596
beta0_black[4]	2.429	0.136	2.165	2.424	2.694
beta0_black[5]	4.559	2.060	1.832	4.109	9.597
beta0_black[6]	4.595	1.940	2.269	4.140	9.685
beta0_black[7]	3.731	1.862	1.558	3.223	8.802
beta0_black[8]	0.949	0.210	0.553	0.947	1.375
beta0_black[9]	2.606	0.230	2.163	2.606	3.060
beta0_black[10]	1.459	0.135	1.190	1.459	1.724
beta0_black[11]	3.482	0.152	3.186	3.486	3.770
beta0_black[12]	4.869	0.179	4.518	4.865	5.220
beta0_black[13]	-0.100	0.231	-0.566	-0.092	0.328
beta0_black[14]	2.849	0.160	2.546	2.852	3.163
beta0_black[15]	1.295	0.154	0.999	1.295	1.601
beta0_black[16]	4.275	0.161	3.957	4.276	4.588
beta2_black[1]	7.223	9.389	0.550	3.306	37.180
beta2_black[2]	0.000	0.000	0.000	0.000	0.000
beta2_black[3]	0.000	0.000	0.000	0.000	0.000
beta2_black[4]	0.000	0.000	0.000	0.000	0.000
beta2_black[5]	0.000	0.000	0.000	0.000	0.000
beta2_black[6]	0.000	0.000	0.000	0.000	0.000
beta2_black[7]	0.000	0.000	0.000	0.000	0.000
beta2_black[8]	0.000	0.000	0.000	0.000	0.000
beta2_black[9]	0.000	0.000	0.000	0.000	0.000
beta2_black[10]	0.000	0.000	0.000	0.000	0.000
beta2_black[11]	0.000	0.000	0.000	0.000	0.000
beta2_black[12]	0.000	0.000	0.000	0.000	0.000
beta2_black[13]	-2.288	1.868	-7.551	-1.696	-0.433
beta2_black[14]	0.000	0.000	0.000	0.000	0.000
beta2_black[15]	0.000	0.000	0.000	0.000	0.000
beta2_black[16]	0.000	0.000	0.000	0.000	0.000
beta3_black[1]	41.770	1.140	39.853	41.928	43.339
beta3_black[2]	25.000	0.000	25.000	25.000	25.000
beta3_black[3]	25.000	0.000	25.000	25.000	25.000
beta3_black[4]	25.000	0.000	25.000	25.000	25.000
beta3_black[5]	25.000	0.000	25.000	25.000	25.000
beta3_black[6]	25.000	0.000	25.000	25.000	25.000
beta3_black[7]	25.000	0.000	25.000	25.000	25.000
beta3_black[8]	25.000	0.000	25.000	25.000	25.000
beta3_black[9]	25.000	0.000	25.000	25.000	25.000
beta3_black[10]	25.000	0.000	25.000	25.000	25.000
beta3_black[11]	25.000	0.000	25.000	25.000	25.000
beta3_black[12]	25.000	0.000	25.000	25.000	25.000
beta3_black[13]	39.273	0.805	37.521	39.365	40.546
beta3_black[14]	25.000	0.000	25.000	25.000	25.000
beta3_black[15]	25.000	0.000	25.000	25.000	25.000
beta3_black[16]	25.000	0.000	25.000	25.000	25.000
beta4_black[1]	-0.263	0.188	-0.644	-0.263	0.110
beta4_black[2]	0.249	0.184	-0.108	0.248	0.602
beta4_black[3]	-0.935	0.200	-1.330	-0.933	-0.542
beta4_black[4]	0.425	0.219	-0.007	0.422	0.853
beta4_black[5]	0.562	1.260	-1.289	0.354	3.517
beta4_black[6]	0.559	1.314	-1.169	0.359	3.527
beta4_black[7]	0.446	1.185	-1.351	0.292	3.178
beta4_black[8]	-0.232	0.317	-0.874	-0.227	0.368
beta4_black[9]	0.864	0.797	-0.271	0.714	2.712
beta4_black[10]	0.056	0.188	-0.315	0.055	0.415
beta4_black[11]	-0.691	0.213	-1.115	-0.690	-0.275
beta4_black[12]	0.170	0.325	-0.463	0.160	0.821
beta4_black[13]	-1.191	0.225	-1.621	-1.197	-0.757
beta4_black[14]	-0.174	0.236	-0.626	-0.178	0.283
beta4_black[15]	-0.897	0.220	-1.333	-0.896	-0.477
beta4_black[16]	-0.592	0.231	-1.039	-0.593	-0.128
mu_beta0_black[1]	1.284	0.925	-0.817	1.334	3.108
mu_beta0_black[2]	2.682	1.082	0.738	2.574	5.160
mu_beta0_black[3]	2.492	0.994	0.266	2.530	4.308
tau_beta0_black[1]	0.623	0.576	0.057	0.447	2.103
tau_beta0_black[2]	0.445	0.595	0.048	0.254	1.918
tau_beta0_black[3]	0.239	0.160	0.052	0.201	0.653
beta0_dsr[11]	-2.893	0.295	-3.483	-2.892	-2.324
beta0_dsr[12]	4.557	0.278	4.011	4.555	5.114
beta0_dsr[13]	-1.359	0.324	-1.957	-1.342	-0.776
beta0_dsr[14]	-3.662	0.503	-4.650	-3.659	-2.684
beta0_dsr[15]	-1.935	0.279	-2.471	-1.936	-1.366
beta0_dsr[16]	-2.992	0.366	-3.740	-2.997	-2.285
beta1_dsr[11]	4.826	0.308	4.232	4.821	5.431
beta1_dsr[12]	6.908	16.061	2.287	4.990	18.997
beta1_dsr[13]	2.875	0.367	2.270	2.857	3.531
beta1_dsr[14]	6.324	0.525	5.279	6.335	7.353
beta1_dsr[15]	3.335	0.286	2.761	3.329	3.894
beta1_dsr[16]	5.807	0.379	5.077	5.807	6.542
beta2_dsr[11]	-8.203	2.296	-13.582	-7.870	-4.552
beta2_dsr[12]	-7.046	2.589	-12.660	-6.859	-2.276
beta2_dsr[13]	-6.458	2.665	-11.803	-6.396	-1.632
beta2_dsr[14]	-6.207	2.640	-11.773	-6.143	-1.784
beta2_dsr[15]	-7.743	2.417	-13.396	-7.501	-3.777
beta2_dsr[16]	-7.906	2.346	-13.487	-7.584	-4.311
beta3_dsr[11]	43.488	0.148	43.213	43.489	43.771
beta3_dsr[12]	33.958	0.736	32.096	34.107	34.827
beta3_dsr[13]	43.248	0.308	42.804	43.194	43.870
beta3_dsr[14]	43.341	0.236	43.072	43.267	43.936
beta3_dsr[15]	43.503	0.188	43.163	43.503	43.840
beta3_dsr[16]	43.442	0.158	43.178	43.429	43.757
beta4_dsr[11]	0.594	0.223	0.179	0.593	1.031
beta4_dsr[12]	0.248	0.443	-0.626	0.247	1.163
beta4_dsr[13]	-0.163	0.225	-0.605	-0.162	0.264
beta4_dsr[14]	0.162	0.251	-0.333	0.167	0.641
beta4_dsr[15]	0.716	0.213	0.310	0.715	1.143
beta4_dsr[16]	0.152	0.229	-0.311	0.152	0.594
beta0_slope[11]	-1.847	0.149	-2.148	-1.846	-1.558
beta0_slope[12]	-4.461	0.254	-4.959	-4.458	-3.974
beta0_slope[13]	-1.330	0.174	-1.686	-1.323	-1.022
beta0_slope[14]	-2.673	0.166	-2.996	-2.673	-2.337
beta0_slope[15]	-1.337	0.147	-1.629	-1.338	-1.056
beta0_slope[16]	-2.739	0.158	-3.047	-2.740	-2.427
beta1_slope[11]	4.484	0.221	4.057	4.484	4.923
beta1_slope[12]	3.989	0.448	3.125	3.987	4.866
beta1_slope[13]	2.681	0.361	2.193	2.640	3.432
beta1_slope[14]	6.318	0.412	5.508	6.307	7.149
beta1_slope[15]	2.999	0.208	2.604	2.995	3.407
beta1_slope[16]	5.279	0.281	4.739	5.275	5.851
beta2_slope[11]	8.630	2.300	5.165	8.303	14.156
beta2_slope[12]	6.677	2.901	1.223	6.697	12.690
beta2_slope[13]	5.468	2.942	0.545	5.350	11.330
beta2_slope[14]	6.520	2.545	2.294	6.417	11.991
beta2_slope[15]	8.169	2.318	4.507	7.834	13.551
beta2_slope[16]	7.800	2.298	4.250	7.470	12.847
beta3_slope[11]	43.462	0.134	43.216	43.460	43.722
beta3_slope[12]	43.358	0.281	42.896	43.323	43.941
beta3_slope[13]	43.443	0.359	42.930	43.390	44.015
beta3_slope[14]	43.262	0.132	43.092	43.230	43.586
beta3_slope[15]	43.495	0.162	43.189	43.494	43.794
beta3_slope[16]	43.374	0.147	43.153	43.351	43.716
beta4_slope[11]	-0.733	0.160	-1.047	-0.736	-0.428
beta4_slope[12]	-1.169	0.475	-2.266	-1.123	-0.345
beta4_slope[13]	0.083	0.162	-0.235	0.085	0.392
beta4_slope[14]	-0.094	0.195	-0.474	-0.096	0.301
beta4_slope[15]	-0.768	0.160	-1.083	-0.769	-0.464
beta4_slope[16]	-0.162	0.178	-0.517	-0.162	0.193
sigma_H[1]	0.202	0.055	0.106	0.198	0.319
sigma_H[2]	0.172	0.030	0.121	0.170	0.235
sigma_H[3]	0.197	0.042	0.123	0.194	0.286
sigma_H[4]	0.420	0.078	0.294	0.412	0.600
sigma_H[5]	0.998	0.209	0.610	0.986	1.421
sigma_H[6]	0.438	0.190	0.079	0.428	0.843
sigma_H[7]	0.309	0.066	0.211	0.299	0.466
sigma_H[8]	0.416	0.091	0.277	0.403	0.603
sigma_H[9]	0.527	0.126	0.328	0.509	0.811
sigma_H[10]	0.211	0.041	0.139	0.207	0.299
sigma_H[11]	0.277	0.046	0.200	0.274	0.380
sigma_H[12]	0.440	0.166	0.207	0.414	0.785
sigma_H[13]	0.215	0.038	0.152	0.213	0.295
sigma_H[14]	0.507	0.093	0.344	0.501	0.707
sigma_H[15]	0.246	0.040	0.179	0.243	0.333
sigma_H[16]	0.226	0.043	0.154	0.221	0.321
lambda_H[1]	3.215	4.576	0.169	1.802	15.137
lambda_H[2]	8.183	7.781	0.813	6.082	27.281
lambda_H[3]	6.431	9.574	0.278	3.149	32.040
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	4.550	11.270	0.037	1.128	34.578
lambda_H[6]	6.468	11.737	0.007	0.848	40.314
lambda_H[7]	0.012	0.009	0.002	0.010	0.034
lambda_H[8]	8.247	9.922	0.111	4.829	34.997
lambda_H[9]	0.015	0.010	0.003	0.013	0.040
lambda_H[10]	0.293	0.440	0.034	0.189	1.058
lambda_H[11]	0.253	0.463	0.011	0.119	1.133
lambda_H[12]	5.207	7.176	0.182	2.835	24.913
lambda_H[13]	3.628	3.252	0.264	2.690	12.440
lambda_H[14]	3.308	4.019	0.201	2.014	14.353
lambda_H[15]	0.024	0.027	0.003	0.016	0.079
lambda_H[16]	0.832	1.170	0.043	0.448	4.145
mu_lambda_H[1]	4.341	1.848	1.280	4.202	8.395
mu_lambda_H[2]	3.860	1.910	0.653	3.721	7.896
mu_lambda_H[3]	3.504	1.810	0.803	3.220	7.687
sigma_lambda_H[1]	8.623	4.242	2.029	8.091	18.050
sigma_lambda_H[2]	8.455	4.586	1.087	7.976	18.248
sigma_lambda_H[3]	6.348	3.956	1.056	5.609	16.233
beta_H[1,1]	6.938	1.034	4.581	7.096	8.592
beta_H[2,1]	9.888	0.497	8.792	9.915	10.760
beta_H[3,1]	7.992	0.762	6.104	8.095	9.165
beta_H[4,1]	9.433	7.833	-7.029	9.576	24.414
beta_H[5,1]	0.156	2.241	-4.535	0.340	3.863
beta_H[6,1]	3.152	3.965	-6.753	4.507	7.620
beta_H[7,1]	0.314	5.846	-12.305	0.852	10.393
beta_H[8,1]	1.313	3.331	-2.105	1.259	3.525
beta_H[9,1]	12.886	5.652	1.495	12.907	24.657
beta_H[10,1]	7.085	1.748	3.488	7.159	10.483
beta_H[11,1]	4.938	3.549	-3.038	5.597	9.919
beta_H[12,1]	2.605	1.047	0.724	2.526	4.902
beta_H[13,1]	9.077	0.915	7.266	9.150	10.513
beta_H[14,1]	2.196	1.050	0.236	2.168	4.295
beta_H[15,1]	-6.096	3.743	-12.975	-6.292	1.772
beta_H[16,1]	3.515	2.658	-0.808	3.229	9.588
beta_H[1,2]	7.907	0.245	7.399	7.914	8.385
beta_H[2,2]	10.024	0.137	9.748	10.026	10.300
beta_H[3,2]	8.955	0.192	8.579	8.956	9.319
beta_H[4,2]	3.589	1.484	0.772	3.545	6.698
beta_H[5,2]	1.964	0.943	0.045	2.007	3.741
beta_H[6,2]	5.689	1.052	3.103	5.845	7.276
beta_H[7,2]	2.689	1.115	0.728	2.620	5.007
beta_H[8,2]	3.024	0.977	1.466	3.142	4.215
beta_H[9,2]	3.524	1.101	1.433	3.507	5.808
beta_H[10,2]	8.193	0.349	7.465	8.205	8.882
beta_H[11,2]	9.798	0.641	8.857	9.674	11.257
beta_H[12,2]	3.940	0.364	3.261	3.932	4.681
beta_H[13,2]	9.119	0.246	8.659	9.113	9.595
beta_H[14,2]	4.015	0.346	3.348	4.014	4.694
beta_H[15,2]	11.355	0.677	10.007	11.383	12.629
beta_H[16,2]	4.530	0.802	3.004	4.505	6.124
beta_H[1,3]	8.450	0.239	8.007	8.440	8.931
beta_H[2,3]	10.070	0.120	9.833	10.069	10.305
beta_H[3,3]	9.615	0.161	9.309	9.612	9.946
beta_H[4,3]	-2.547	0.889	-4.383	-2.522	-0.833
beta_H[5,3]	3.834	0.610	2.567	3.847	5.020
beta_H[6,3]	7.937	1.184	6.323	7.579	10.505
beta_H[7,3]	-2.802	0.671	-4.125	-2.802	-1.529
beta_H[8,3]	5.225	0.456	4.653	5.172	6.064
beta_H[9,3]	-2.880	0.743	-4.420	-2.854	-1.451
beta_H[10,3]	8.688	0.279	8.142	8.688	9.215
beta_H[11,3]	8.525	0.292	7.880	8.549	9.028
beta_H[12,3]	5.259	0.315	4.502	5.299	5.772
beta_H[13,3]	8.838	0.174	8.479	8.845	9.169
beta_H[14,3]	5.715	0.277	5.109	5.735	6.207
beta_H[15,3]	10.363	0.318	9.745	10.364	10.989
beta_H[16,3]	6.243	0.611	4.894	6.315	7.243
beta_H[1,4]	8.260	0.180	7.873	8.268	8.582
beta_H[2,4]	10.130	0.119	9.881	10.138	10.339
beta_H[3,4]	10.120	0.159	9.782	10.134	10.404
beta_H[4,4]	11.817	0.451	10.910	11.828	12.714
beta_H[5,4]	5.480	0.740	4.267	5.398	7.152
beta_H[6,4]	6.991	0.932	4.876	7.280	8.252
beta_H[7,4]	8.293	0.354	7.594	8.295	8.964
beta_H[8,4]	6.713	0.238	6.259	6.725	7.114
beta_H[9,4]	7.217	0.461	6.324	7.213	8.151
beta_H[10,4]	7.724	0.237	7.278	7.719	8.225
beta_H[11,4]	9.384	0.198	9.002	9.383	9.770
beta_H[12,4]	7.142	0.214	6.722	7.138	7.586
beta_H[13,4]	9.044	0.142	8.759	9.047	9.317
beta_H[14,4]	7.733	0.220	7.316	7.727	8.177
beta_H[15,4]	9.473	0.235	9.033	9.472	9.921
beta_H[16,4]	9.346	0.241	8.921	9.331	9.853
beta_H[1,5]	8.989	0.141	8.707	8.992	9.253
beta_H[2,5]	10.783	0.091	10.610	10.780	10.966
beta_H[3,5]	10.914	0.173	10.614	10.904	11.266
beta_H[4,5]	8.372	0.470	7.494	8.354	9.362
beta_H[5,5]	5.432	0.579	4.061	5.480	6.463
beta_H[6,5]	8.832	0.639	7.928	8.674	10.320
beta_H[7,5]	6.736	0.344	6.098	6.730	7.413
beta_H[8,5]	8.218	0.206	7.886	8.206	8.634
beta_H[9,5]	8.189	0.463	7.248	8.204	9.089
beta_H[10,5]	10.102	0.226	9.636	10.104	10.542
beta_H[11,5]	11.506	0.221	11.073	11.504	11.935
beta_H[12,5]	8.485	0.201	8.102	8.484	8.878
beta_H[13,5]	10.012	0.127	9.775	10.013	10.264
beta_H[14,5]	9.199	0.229	8.777	9.193	9.670
beta_H[15,5]	11.161	0.246	10.677	11.156	11.654
beta_H[16,5]	9.913	0.184	9.531	9.919	10.254
beta_H[1,6]	10.175	0.186	9.842	10.161	10.601
beta_H[2,6]	11.511	0.109	11.302	11.511	11.723
beta_H[3,6]	10.814	0.159	10.472	10.821	11.103
beta_H[4,6]	12.908	0.837	11.183	12.918	14.491
beta_H[5,6]	5.902	0.584	4.747	5.897	7.062
beta_H[6,6]	8.821	0.688	6.965	8.961	9.774
beta_H[7,6]	9.894	0.564	8.787	9.880	10.983
beta_H[8,6]	9.523	0.268	8.986	9.544	9.954
beta_H[9,6]	8.470	0.788	6.893	8.475	10.003
beta_H[10,6]	9.496	0.313	8.825	9.518	10.040
beta_H[11,6]	10.820	0.346	10.087	10.833	11.453
beta_H[12,6]	9.388	0.257	8.908	9.376	9.928
beta_H[13,6]	11.047	0.167	10.748	11.036	11.397
beta_H[14,6]	9.839	0.290	9.264	9.845	10.403
beta_H[15,6]	10.846	0.423	9.986	10.846	11.671
beta_H[16,6]	10.544	0.235	10.055	10.549	11.001
beta_H[1,7]	10.878	0.848	8.825	10.983	12.207
beta_H[2,7]	12.208	0.437	11.306	12.211	13.047
beta_H[3,7]	10.568	0.663	9.082	10.628	11.681
beta_H[4,7]	2.448	4.328	-5.824	2.395	11.148
beta_H[5,7]	6.461	1.756	3.200	6.406	10.399
beta_H[6,7]	9.743	2.486	5.046	9.654	16.250
beta_H[7,7]	10.419	2.824	4.919	10.441	15.801
beta_H[8,7]	10.964	0.951	9.460	10.923	12.559
beta_H[9,7]	4.460	3.998	-3.162	4.452	12.622
beta_H[10,7]	9.876	1.447	7.336	9.744	13.182
beta_H[11,7]	10.961	1.705	7.681	10.864	14.646
beta_H[12,7]	10.023	0.965	7.857	10.090	11.646
beta_H[13,7]	11.643	0.779	9.722	11.740	12.861
beta_H[14,7]	10.403	0.960	8.377	10.445	12.123
beta_H[15,7]	11.963	2.222	7.669	11.946	16.317
beta_H[16,7]	12.239	1.233	10.157	12.085	14.943
beta0_H[1]	8.406	12.282	-17.337	8.513	32.156
beta0_H[2]	10.535	6.328	-2.352	10.624	23.291
beta0_H[3]	9.852	9.749	-9.608	9.788	30.344
beta0_H[4]	2.245	182.045	-375.184	1.291	379.083
beta0_H[5]	3.809	24.589	-43.294	4.039	49.669
beta0_H[6]	6.958	52.830	-107.047	7.481	111.558
beta0_H[7]	6.910	140.303	-275.120	4.704	296.527
beta0_H[8]	5.932	27.134	-16.431	6.478	26.270
beta0_H[9]	6.202	120.495	-240.287	5.752	246.422
beta0_H[10]	7.449	33.640	-62.147	7.847	75.656
beta0_H[11]	8.773	51.466	-104.705	9.400	116.505
beta0_H[12]	6.488	11.375	-17.152	6.689	27.979
beta0_H[13]	9.790	10.907	-10.576	10.030	29.485
beta0_H[14]	7.142	12.289	-16.505	7.008	31.401
beta0_H[15]	7.275	104.678	-211.610	5.947	213.295
beta0_H[16]	9.046	25.997	-39.522	8.224	64.556